Recovery Type A Posteriori Error Estimates

恢复类型 A 后验误差估计

• 批准号: 0311807
• 负责人: Zhimin Zhang
• 金额: $ 17.25万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0311807&HistoricalAwards=false
• 关键词: Recovery; Type; Posteriori; Error; Estimates

Zhang The investigator studies a posteriori error estimates forthe numerical solution of partial differential equations. Hedevelops general mathematical theory for recovery type aposteriori error estimates and explores a new gradient recoverytechnique and associated error estimator that has betterproperties than the existing ones. Some recent mathematicaltheory in finite element superconvergence, asymptotic regularity,as well as improved interior analysis, is employed in theproject. Numerical solutions of differential equations are essentialin all areas of science and engineering. But the numericalsolutions are often less accurate than one desires. It istherefore important to estimate the error and to use thatestimate to improve the accuracy. Error estimation is essentialfor effective and reliable computation. Recovery type aposteriori error estimates are post-processing techniques thatuse a numerical solution produced by some base method to produceapproximations that are of higher order of accuracy than the basemethod solution, and that combine the two solutions to estimatethe error in the approximate solution. The techniques are commonbut not theoretically understood or justified, especially fornonuniform meshes. The investigator studies these methods anddevelops a new kind of recovery type error estimator that offerssome advantages over present alternatives. The project fills agap between engineering practice and mathematical theoreticaldevelopment. The project includes training of graduate students.There are interdisciplinary connections with engineers and otherscientific computing disciplines, and with industry.

张研究者研究了部分微分方程的数值解的后验错误估计。 HEDE开发用于恢复类型的aposteriori误差估算的一般数学理论，并探索了一种新的梯度恢复技术和相关的误差估计器，其具有比现有的梯度更好。 该项目中采用了有限元超级范围的一些数学理论，渐近规则性以及改进的内部分析。 微分方程的数值解决方案是科学和工程的所有领域的必需方程。 但是，数值施加通常不如一种欲望准确。 因此，重要的是要估计误差并使用该误差来提高准确性。 错误估计对于有效且可靠的计算至关重要。 恢复类型的aposteriori误差估计是后处理技术，该技术使用某些基本方法产生的数值解决方案来产生比基emethod解决方案更高的准确度较高的pyproximation，并且结合了两种解决方案以估计近似解决方案中的误差。 这些技术是常见的，但理论上并非理解或合理，尤其是肾均匀网格。 研究者研究这些方法并开发了一种新型的恢复类型误差估计器，该估计量与当前替代方案具有优势。 该项目填补了工程实践与数学理论发展之间的AGAP。 该项目包括对研究生的培训。